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<a class="navbar-brand" href="week41-bs.html">Week 41 Constructing a Neural Network code, Tensor flow and start Convolutional Neural Networks</a>
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<!-- navigation toc: --> <li><a href="._week41-bs001.html#plan-for-week-41" style="font-size: 80%;">Plan for week 41</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs002.html#videos-on-neural-networks" style="font-size: 80%;">Videos on Neural Networks</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs003.html#review-of-the-back-propagation-algorithm" style="font-size: 80%;">Review of the back propagation algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs004.html#setting-up-the-back-propagation-algorithm" style="font-size: 80%;">Setting up the Back propagation algorithm</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs005.html#setting-up-a-multi-layer-perceptron-model-for-classification" style="font-size: 80%;">Setting up a Multi-layer perceptron model for classification</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs006.html#defining-the-cost-function" style="font-size: 80%;">Defining the cost function</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs007.html#example-binary-classification-problem" style="font-size: 80%;">Example: binary classification problem</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs008.html#the-softmax-function" style="font-size: 80%;">The Softmax function</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs009.html#developing-a-code-for-doing-neural-networks-with-back-propagation" style="font-size: 80%;">Developing a code for doing neural networks with back propagation</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs036.html#collect-and-pre-process-data" style="font-size: 80%;">Collect and pre-process data</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs011.html#train-and-test-datasets" style="font-size: 80%;">Train and test datasets</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs012.html#define-model-and-architecture" style="font-size: 80%;">Define model and architecture</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs013.html#layers" style="font-size: 80%;">Layers</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs014.html#weights-and-biases" style="font-size: 80%;">Weights and biases</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs015.html#feed-forward-pass" style="font-size: 80%;">Feed-forward pass</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs016.html#matrix-multiplications" style="font-size: 80%;">Matrix multiplications</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs017.html#choose-cost-function-and-optimizer" style="font-size: 80%;">Choose cost function and optimizer</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs018.html#optimizing-the-cost-function" style="font-size: 80%;">Optimizing the cost function</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs019.html#regularization" style="font-size: 80%;">Regularization</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs020.html#matrix-multiplication" style="font-size: 80%;">Matrix multiplication</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs021.html#improving-performance" style="font-size: 80%;">Improving performance</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs022.html#full-object-oriented-implementation" style="font-size: 80%;">Full object-oriented implementation</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs023.html#evaluate-model-performance-on-test-data" style="font-size: 80%;">Evaluate model performance on test data</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs024.html#adjust-hyperparameters" style="font-size: 80%;">Adjust hyperparameters</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs027.html#visualization" style="font-size: 80%;">Visualization</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs026.html#scikit-learn-implementation" style="font-size: 80%;">scikit-learn implementation</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs027.html#visualization" style="font-size: 80%;">Visualization</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs028.html#testing-our-code-for-the-xor-or-and-and-gates" style="font-size: 80%;">Testing our code for the XOR, OR and AND gates</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs029.html#the-and-and-xor-gates" style="font-size: 80%;">The AND and XOR Gates</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs030.html#representing-the-data-sets" style="font-size: 80%;">Representing the Data Sets</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs031.html#setting-up-the-neural-network" style="font-size: 80%;">Setting up the Neural Network</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs032.html#the-code-using-scikit-learn" style="font-size: 80%;">The Code using Scikit-Learn</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs033.html#building-neural-networks-in-tensorflow-and-keras" style="font-size: 80%;">Building neural networks in Tensorflow and Keras</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs034.html#tensorflow" style="font-size: 80%;">Tensorflow</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs035.html#using-keras" style="font-size: 80%;">Using Keras</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs036.html#collect-and-pre-process-data" style="font-size: 80%;">Collect and pre-process data</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs037.html#the-breast-cancer-data-now-with-keras" style="font-size: 80%;">The Breast Cancer Data, now with Keras</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs038.html#the-mathematics-of-neural-networks" style="font-size: 80%;">The Mathematics of Neural Networks</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs039.html#fine-tuning-neural-network-hyperparameters" style="font-size: 80%;">Fine-tuning neural network hyperparameters</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs040.html#hidden-layers" style="font-size: 80%;">Hidden layers</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs041.html#which-activation-function-should-i-use" style="font-size: 80%;">Which activation function should I use?</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs042.html#is-the-logistic-activation-function-sigmoid-our-choice" style="font-size: 80%;">Is the Logistic activation function (Sigmoid) our choice?</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs043.html#the-derivative-of-the-logistic-funtion" style="font-size: 80%;">The derivative of the Logistic funtion</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs044.html#the-relu-function-family" style="font-size: 80%;">The RELU function family</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs045.html#which-activation-function-should-we-use" style="font-size: 80%;">Which activation function should we use?</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs046.html#more-on-activation-functions-output-layers" style="font-size: 80%;">More on activation functions, output layers</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs047.html#batch-normalization" style="font-size: 80%;">Batch Normalization</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs048.html#dropout" style="font-size: 80%;">Dropout</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs049.html#gradient-clipping" style="font-size: 80%;">Gradient Clipping</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs050.html#a-very-nice-website-on-neural-networks" style="font-size: 80%;">A very nice website on Neural Networks</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs051.html#a-top-down-perspective-on-neural-networks" style="font-size: 80%;">A top-down perspective on Neural networks</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs052.html#limitations-of-supervised-learning-with-deep-networks" style="font-size: 80%;">Limitations of supervised learning with deep networks</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs053.html#overarching-views-a-personal-note" style="font-size: 80%;">Overarching Views, a personal note</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs054.html#using-automatic-differentiation" style="font-size: 80%;">Using Automatic differentiation</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs055.html#solving-odes-with-deep-learning" style="font-size: 80%;">Solving ODEs with Deep Learning</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs056.html#ordinary-differential-equations" style="font-size: 80%;">Ordinary Differential Equations</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs099.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs058.html#minimization-process" style="font-size: 80%;">Minimization process</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs059.html#minimizing-the-cost-function-using-gradient-descent-and-automatic-differentiation" style="font-size: 80%;">Minimizing the cost function using gradient descent and automatic differentiation</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs060.html#example-exponential-decay" style="font-size: 80%;">Example: Exponential decay</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs061.html#the-function-to-solve-for" style="font-size: 80%;">The function to solve for</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs099.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs063.html#setup-of-network" style="font-size: 80%;">Setup of Network</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs064.html#reformulating-the-problem" style="font-size: 80%;">Reformulating the problem</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs065.html#more-technicalities" style="font-size: 80%;">More technicalities</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs090.html#more-details" style="font-size: 80%;">More details</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs067.html#a-possible-implementation-of-a-neural-network" style="font-size: 80%;">A possible implementation of a neural network</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs068.html#technicalities" style="font-size: 80%;">Technicalities</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs069.html#final-technicalities-i" style="font-size: 80%;">Final technicalities I</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs070.html#final-technicalities-ii" style="font-size: 80%;">Final technicalities II</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs071.html#final-technicalities-iii" style="font-size: 80%;">Final technicalities III</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs072.html#final-technicalities-iv" style="font-size: 80%;">Final technicalities IV</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs073.html#back-propagation" style="font-size: 80%;">Back propagation</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs074.html#gradient-descent" style="font-size: 80%;">Gradient descent</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs075.html#the-code-for-solving-the-ode" style="font-size: 80%;">The code for solving the ODE</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs076.html#the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer" style="font-size: 80%;">The network with one input layer, specified number of hidden layers, and one output layer</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs077.html#example-population-growth" style="font-size: 80%;">Example: Population growth</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs078.html#setting-up-the-problem" style="font-size: 80%;">Setting up the problem</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs099.html#the-trial-solution" style="font-size: 80%;">The trial solution</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs080.html#the-program-using-autograd" style="font-size: 80%;">The program using Autograd</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs081.html#using-forward-euler-to-solve-the-ode" style="font-size: 80%;">Using forward Euler to solve the ODE</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs082.html#example-solving-the-one-dimensional-poisson-equation" style="font-size: 80%;">Example: Solving the one dimensional Poisson equation</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs094.html#setting-up-the-network-using-autograd-the-trial-solution" style="font-size: 80%;">Setting up the network using Autograd; The trial solution</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs095.html#why-the-jacobian" style="font-size: 80%;">Why the jacobian?</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs096.html#setting-up-the-network-using-autograd-the-full-program" style="font-size: 80%;">Setting up the network using Autograd; The full program</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs097.html#example-solving-the-wave-equation-with-neural-networks" style="font-size: 80%;">Example: Solving the wave equation with Neural Networks</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs098.html#the-problem-to-solve-for" style="font-size: 80%;">The problem to solve for</a></li>
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<!-- navigation toc: --> <li><a href="._week41-bs101.html#solving-the-wave-equation-the-full-program-using-autograd" style="font-size: 80%;">Solving the wave equation - the full program using Autograd</a></li>
<!-- navigation toc: --> <li><a href="._week41-bs102.html#resources-on-differential-equations-and-deep-learning" style="font-size: 80%;">Resources on differential equations and deep learning</a></li>
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<h1>Week 41 Constructing a Neural Network code, Tensor flow and start Convolutional Neural Networks</h1>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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[1] <b>Department of Physics, University of Oslo</b>
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[2] <b>Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University</b>
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<h4>Oct 18, 2022</h4>
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